The structure and phase behavior of a two-dimensional system with purely repulsive core-softened and long-range interactions are studied using Monte Carlo computer simulations. The pair interactions are of the form, u(r)= 4epsilon[(sigma/r)12 -(sigma/r)6] + epsilon'(sigma/r)3, with the energy parameter, epsilon'= (8 sq.r 6/9)epsilon chosen to give a stationary point of inflection in the pair potential at r=6 1/6 sigma. This potential approximates the effective interparticle interactions for a two-dimensional dipolar system in a strong field aligned perpendicular to the plane. The low-temperature portion of the phase diagram is sketched out, and the static properties of the various phases are analyzed in some detail. At low temperatures a variety of interesting states are in evidence, including: fluids with chainlike, striped, and 6–10 sided polygon structural motifs; low-density and highdensity triangular crystalline phases; and defective Kagome´ lattices. It is shown that clustering is driven by the presence of the repulsive shoulder in the pair potential. Other features, such as the presence of a disordered phase with a network structure, are due to the long-range (1/r3) repulsive tail in the potential. The relevance of the simulation results to experimental work, including materials synthesis, is briefly discussed.